He has left Forest after just five months at the club.
Former Manchester United captain Keane said: "Working with Martin over the last few years has been a magnificent experience, one of my greatest in football both as a player and a coach and one I want to personally thank him for."
A club statement added: "Roy would like to express his gratitude to the club's owner, board of directors, the staff, the players and in particular manager Martin O'Neill for the opportunity to return to The City Ground.
"The former Red would also like to place on record his appreciation to the supporters who have welcomed him back so warmly since his appointment in January.
"Everyone at the club would like to wish Roy the very best in the next stage of his career."